Binomial Theorem

Math for CS · Axiom Academy

Expanding powers of binomials -- connecting algebra to counting The binomial theorem gives us a formula for expanding (a + b)^n without multiplying it out step by step. When you expand (a+b)^n = (a+b)(a+b) (a+b) , you pick either a or b from each of the n factors and multiply them together. This is why "binomial coefficients" are called that -- they literally are the coefficients that appear in binomial expansions. By substituting specific values for a and b , we can derive powerful identities. The binomial theorem isn't just algebra -- it's a counting tool. Answer: 0 + 2 + 4 + 6 + 8 + 10 Using the identity from a=1, b=-1 : the sum of even-index binomial coefficients equals 2^ 10 2 = 512 . The x^3 term comes from k = 2 (picking b = -3 twice): The binomial theorem generalizes to more than two terms:

This is the written version of the interactive lesson above. See the full Math for CS course.